Nice to Switzerland

There is one daily direct train from Nice to Geneva, times here (page 3): http://www.tgv-lyria.com/sites/default/files/pdf/BROCHURES_CO/frequencies-timetable-2017s1-ch_fr-tgv-lyria-en.pdf
But, depending where in Switzerland, it may be quicker to go via Milan. Also consider flying, as it is a long (if scenic) trip by train.

1) What travel pass? There are many different ones. A multi-country (France + Switz) pass is almost certainly not worth it just for one trip.
2) Again what pass? A Pass valid in France will cover you up to the French/Swiss border. A pass valid in Switzerland will cover you after the border. But, if you go via Milan, that is Italy.
3) You need to do the arithmetic yourself. There are 3 options
a) A Swiss pass, nothing else to pay.
b) A Swiss half price card, plus half price tickets for each trip.
c) Full price tickets for each trip.

You need to list all your proposed trips, price them up ( www.sbb.ch ) and decide whether option (a), (b) or (c) is best for you.
And, if you are just taking one trip in France, from Nice to Switzerland (possibly via Italy), just buy a cheap advance purchase ticket.

Thank you Chris for the comprehensive and quick reply.
I will purchase the ticket separately from nice to interlaken, and get the swiss travel pass to cover all travel in Switzerland.

Thank you kind sir!

It you intend to buy a Swiss pass, you don't need to pay for a ticket all the way from Nice to Interlaken, assuming you can get hold of the Swiss pass before you cross the border. Instead, just buy a ticket from Nice to the Swiss border. Swiss trains are fabulous but costly if you pay full price. If you take the Italian route, a full-fare ticket for the Swiss leg will be about CHF 45 (over $45). No sense paying separately to get all the way to Interlaken when the pass would cover the Swiss part of the journey.

If you choose the Nice-Geneva TGV train, then Geneva is your border station, from where you can start using a Swiss Travel pass for all the Swiss connections.

The cheapest tickets for this TGV are currently for sale for travel through March 3, so your date could become available soon, before the common "3 months ahead" plan.

I second what acraven says. If you are getting a Swiss pass, AND it covers your arrival day, you only need to buy a ticket up to the Swiss railway boundary.
Note "boundary" in this case means the boundary between the railway companies. This may be before or after the political border. See the map here, which shows exactly what is and isn't covered by a Swiss pass: https://www.swisspasses.com/railpass/overviewmap_en.pdf
If travelling via Geneva, the railway boundary is Geneva, inside Switzerland. If travelling via Milan to Brig, the railway boundary is Domodossola, well before the national border.